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High-Dimensional Canonical Correlation Analysis

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  • Anna Bykhovskaya
  • Vadim Gorin

Abstract

This paper studies high-dimensional canonical correlation analysis (CCA) with an emphasis on the vectors that define canonical variables. The paper shows that when two dimensions of data grow to infinity jointly and proportionally, the classical CCA procedure for estimating those vectors fails to deliver a consistent estimate. This provides the first result on the impossibility of identification of canonical variables in the CCA procedure when all dimensions are large. As a countermeasure, the paper derives the magnitude of the estimation error, which can be used in practice to assess the precision of CCA estimates. Applications of the results to cyclical vs. non-cyclical stocks and to a limestone grassland data set are provided.

Suggested Citation

  • Anna Bykhovskaya & Vadim Gorin, 2023. "High-Dimensional Canonical Correlation Analysis," Papers 2306.16393, arXiv.org, revised Aug 2023.
    • Handle: RePEc:arx:papers:2306.16393
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    References listed on IDEAS

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    Cited by:

    1. Paulo M. M. Rodrigues & Mirjam Salish & Nazarii Salish, 2024. "Saving for sunny days: The impact of climate (change) on consumer prices in the euro area," Papers 2401.03740, arXiv.org.

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